CM chondrites are the most common type of hydrated meteorites, making up ~1.5% of all falls. Whereas most CM chondrites experienced only low-temperature (~0{deg}C-120{deg}C) aqueous alteration, the existence of a small fraction of CM chondrites that suffered both hydration and heating complicates our understanding of the early thermal evolution of the CM parent body(ies). Here, we provide new constraints on the collisional and thermal history of CM-like bodies from a comparison between newly acquired spectral measurements of main-belt Ch/Cgh-type asteroids (70 objects) and existing laboratory spectral measurements of CM chondrites. It first appears that the spectral variation observed among CM-like bodies is essentially due to variations in the average regolith grain size. Second, the spectral properties of the vast majority (unheated) of CM chondrites resemble both the surfaces and the interiors of CM-like bodies, implying a "low" temperature (100km) - supposedly primordial - Ch/Cgh-type main-belt asteroids likely expose the interiors of the primordial CM parent bodies, a possible consequence of impacts by small asteroids (D<10km) in the early solar system.